Various techniques for supervising units in a communications network are known to the person skilled in the art. A supervisor unit is generally responsible for supervising a limited number of units. For a communications network operator, setting up supervision of a large number of (approximately one million) terminal units disposed on user premises causes a problem with scaling up, especially for the management of alarms sent back from the terminal units to the supervisor unit. While operating, these terminal units can send unsolicited alarms. By way of illustrative example, the document RFC 3164 defines a Syslog alarm that notifies a supervisor unit of an event such as the occurrence of an anomaly. The alarm described in the document RFC 3164 contains dedicated severity and facility fields from which a priority level of the alarm can be deduced. On reception of a priority alarm, the supervisor unit can analyze it and act accordingly. However, this management method is not well suited to a vast installed base of terminal units. In the event of a general anomaly affecting all or at least a major portion of the units of the installed base, there can be an avalanche of alarms that are difficult to manage in real time for the supervisor unit and a higher priority alarm can be buried in an avalanche of lower priority alarms. Moreover, the occurrence of an avalanche of lower priority alarms can also require fast analysis by the operator.